Preheat oven to 350°F. Spread out pistachios on a small rimmed baking sheet; toast, stirring occasionally until golden brown, 6–8 minutes. Coarsely chop once cool enough to handle.
Combine garlic, raisins, and vinegar in a large bowl and let sit 1 hour. Chop carrots and beets, or if you have a food processor, use the juienne tool here!
Remove and discard garlic from raisin mixture. Add carrots, beets, pistachios, parsley, mint, lemon juice, and red pepper flakes; season with salt and pepper and toss to combine. Add oil and toss gently. For best flavor, make at least one hour in advance.